Joint security and robustness enhancement for quantization...

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY, VOL. 13, NO. 8, AUGUST 2003 831

Joint Security and Robustness Enhancement forQuantization Based Data Embedding

Min Wu, Member, IEEE

Abstract—This paper studies joint security and robustnessenhancement of quantization-based data embedding for multi-media authentication applications. We present analysis showingthat through a lookup table (LUT) of nontrivial run that mapsquantized multimedia features randomly to binary data, theprobability of detection error can be considerably smaller thanthe traditional quantization embedding. We quantify the securitystrength of LUT embedding and enhance its robustness throughdistortion compensation. Introducing a joint security and capacitymeasure, we show that the proposed distortion-compensated LUTembedding provides joint enhancement of security and robustnessover the traditional quantization embedding.

Index Terms—Data hiding, digital watermarking, distortioncompensation, joint security and robustness enhancement, lookuptable (LUT) embedding.

I. INTRODUCTION

DATA HIDING in multimedia signals has been an activeresearch area in recent years. One potential application is

to use the embedded data to verify whether or not a multimediahost signal has been tampered with [1], [2]. The data-embed-ding mechanism for these authentication applications should besecure enough to prevent an adversary from forging the em-bedded data at his/her will [3]. In addition, semi-fragilenessis often preferred to allow for distinguishing content changesversus noncontent changes. Robustness against moderate com-pression is desirable as the multimedia data with authenticationwatermark embedded in may inevitably go through lossy com-pression, such as in the emerging application of building trust-worthy digital cameras [4]–[7]. In this paper, we focus on jointlyenhancing the robustness and security of core embedding mech-anisms that can be used as building blocks for authentication.

While spread-spectrum techniques have been widely used toembed a small number of bits robustly in multimedia signals[8], quantization-based embedding is more common for suchhigh-rate data-hiding applications as authentication. A populartechnique, often known as odd–even embedding [9] or ditheredmodulation [10], is to choose a quantization step sizeandround a feature, which can be a sample or a coefficient of thehost signal, to the closest even multiples ofto embed a “0”and to odd multiples to embed a “1”. Motivated by Costa’s in-formation theoretical result [11], distortion compensation has

Manuscript received December 23, 2002; revised May 19, 2003. This re-search was supported in part by research grants from the U.S. National ScienceFoundation CCR-0133704 (CAREER) and the Minta Martin Foundation.

The author is with the Department of Electrical and Computer Engi-neering, University of Maryland, College Park, MD 20742, USA (e-mail:[email protected]).

Digital Object Identifier 10.1109/TCSVT.2003.815951

been proposed to be incorporated into quantization-based em-bedding [10], [12]–[14], where the quantization embedding re-sult is combined linearly with the host signal to form a water-marked signal. Using the optimal compensation factor that isa function of watermark-to-noise ratio (WNR), distortion com-pensated version of odd–even embedding can reach higher pay-load than the odd–even embedding alone.

One of the main problems of quantization-based embeddingis security. An adversary who knows the embedding algorithmcan change the embedded data at his/her will, which presentsconcerns of counterfeiting attacks on authentication [3]. Thereare three directions in which to alleviate this security problem.The first is to encrypt the data to be embedded using a securecipher such as AES and RSA [15]. The second approach is toprovide security to feature extraction, such as deriving featuresthrough projecting a set of samples/coefficients along a direc-tion specified by a key [16], [17]. The third approach is to addsecurity to the embedding mechanism itself to make it difficultfor an adversary to embed a specific bit at his/her will. Since thefirst and second approaches involve multiple samples or coeffi-cients, they cannot always allow the localization of tamperedregions to fine scale, which is a desirable feature for authen-tication [2], [4]. In this paper, we concentrate on the third ap-proach. More specifically, we propose new enhancement strate-gies for quantization-based embedding, which leads to joint im-provement of security and robustness. It can also be combinedwith the other two approaches to further enhance the securitystrength.

Our proposed approach is built on top of a general embed-ding technique known as look-up table (LUT) embedding. Apixel-domain LUT embedding scheme was proposed by Yeungand Mintzer [2], and was extended to quantization-based em-bedding in a transform domain in our earlier work [4]. The pro-prietary LUT can be generated from a cryptographic key andadd security to embedding. With the same quantization stepsize, the LUT embedding generally introduces larger distortionthan the traditional odd–even embedding, making it less pop-ular. In this paper, however, we present analysis showing that atthe same WNR, the probability of detection error for LUT em-bedding can be smaller than the odd–even embedding. We fur-ther quantify the security strength of LUT embedding and ana-lyze the effect of distortion compensation on it. As will be seen,our proposed distortion compensated LUT embedding providesjoint enhancement of security and robustness over the traditionalquantization embedding.

The paper is organized as the follows. We begin with a generalformulation of LUT embedding in Section II. The security androbustness of LUT embedding are analyzed in Section III and

1051-8215/03$17.00 © 2003 IEEE

832 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY, VOL. 13, NO. 8, AUGUST 2003

Section IV, respectively. We then propose and analyze distortioncompensated LUT embedding in Section V and demonstrate itscapability of joint enhancement of security and robustness. Sec-tion VI presents experimental results on images. Finally, conclu-sions are drawn in Section VII.

II. LUT EMBEDDING

We focus on quantization-based embedding in scalar featuresand use uniform quantizers in this paper. A proprietary LUT

is generated beforehand. The table maps every possiblequantized feature value randomly to “1” or “0” with a constraintthat the runs of “1” and “0” are limited in length. To embed a“1” in a feature, the feature is simply replaced by its quantizedversion if the entry of the table corresponding to that featureis also a “1”. If the entry of the table is a “0”, then the fea-ture is changed to its nearest neighboring values for which theentry is “1”. The embedding of a “0” is similar. For example,we consider a uniform quantizer1 with quantization step size

and a look-up table. To embed a “1” to a coefficient

“84”, we round it to the nearest multiple of ten such that themultiple is mapped to “1” by the LUT. In this case, we foundthat “90” satisfies this requirement and use “90” as the water-marked pixel value. Similarly, to embed a “0” in this pixel, weround it to “80”.

This embedding process can be abstracted into the followingformula, where is the original feature, is the marked one,

is a bit to be embedded in, and is the quantizationoperation

.(1)

Here,. The extraction of the embedded data is by looking up the

table

(2)

where is the extracted bit.

III. QUANTIFYING THE SECURITY OFLUT EMBEDDING

During the process of LUT embedding by (1), whendoes not match the bit to be embedded,

we need to find a nearby entry in LUT that is mapped to.As such, the run of “1” and “0” entries of an LUT need to beconstrained to avoid excessive modification on the feature. Wedenote the maximum allowable run of “1” and “0” as. Toanalyze security as a function of, we start with the case of

, which leads to only two possible tables

(if i is even),(if i is odd),

(if i is even)(if i is odd).

1For a uniform quantizer with quantization step sizeq considered in thispaper, the quantization operationQuant(x) is to roundx to the nearest in-teger multiples ofq.

This is essentially the odd–even embedding [9] or the ditheredmodulation embedding [10]. Since there is little uncertainty inthe table, unauthorized persons can easily manipulate the em-bedded data, and/or change some feature values while retainingthe embedded values. As we discussed earlier in this paper, theodd–even embedding, or equivalently the choice of , is notappropriate for authentication applications if no other securitymeasures, such as a careful design of what data to embed, aretaken.

When is greater than 1, the number of LUTs satisfying therun constraint can be computed from the recursive relation pre-sented in the following theorem.

Theorem 1: Let be the number of -ary LUTs thathave a total of entries and runs no greater than. Then, for

(3)

Proof: See the Appendix.

Corollary 1: Construct a binary LUT as follows:1) equiprobably initialize each of the first two entries to0 or 1 and 2) generate the remaining entries with maximumallowable run of 2. Let the number of-entry LUTs that satisfythe above conditions be . Then, is equals to twice theFibonacci series for , and ,

, .As an example of this corollary, we look at binary LUT with a

length of 256 and maximum run of 2. The total number of suchLUTs is on the order of , which is a significant increasefrom only two possible tables for run 1.

We further quantify the uncertainty of LUT embedding byidentifying the generation process of binary LUT as a-stateMarkov chain illustrated in Fig. 1(a). Defining a state vector as[ , ], the state transition ma-trix of this Markov chain is

(4)We can show that the stationary probability of both andstates is

(5)

WU: JOINT SECURITY AND ROBUSTNESS ENHANCEMENT FOR QUANTIZATION BASED DATA EMBEDDING 833

(a)

(b)

Fig. 1. Quantifying the uncertainty in LUT table generation. (a) A Markovchain model for LUT table generation, where the transition probability is 1/2for solid arrow lines and 1 for dash arrow lines. (b) The entropy rate of LUTtable as a function of the maximum allowable runr.

for , and the entropy rate of the stationary processis [18]

(6)

For example, in the case of maximum allowable run , theLUT generation process is a 4-state Markov chain with transi-tion matrix

(7)

The stationary probability is , and theentropy rate is 2/3 bit. In contrast, the entropy rate with max-imum run of 1 (or equivalently, the odd-even embedding) is 0bit. We plot the entropy rate as a function ofin Fig. 1(b), whichindicates that the uncertainty of LUT has increased significantlywith a slight increase of the maximum allowable run.

It is important to note that the security quantified in this sec-tion measures how difficult an adversary can manipulate thedata embedded in a watermarked feature with the knowledgeof only this feature. We are interested in how much uncertaintya basic embedding mechanism can offer to each individual fea-ture. Zooming into an LUT embedding mechanism that is al-ready sufficiently secure at the individual feature level, anothersecurity aspect addresses how feasible it is for an adversary toderive the LUT from a number of watermarked features. Sucha threat can be alleviated by introducing location dependency

so that effectively different LUTs are used for different features[3]. Interested readers can refer to [3] for details.

IV. ROBUSTNESSANALYSIS ON LUT EMBEDDING

Though bringing higher security, the increase in the allowablerun will inevitably lead to larger embedding distortion when afeature value of the host signal is not mapped by LUT to the bitto be embedded. In this section, we analyze the mean squareddistortion introduced by LUT embedding and its probability ofdetection error under additive white Gaussian noise.

A. Distortion Incurred by Embedding

The mean squared distortion incurred by LUT embeddingwith binary LUT and maximum allowable run is derivedas the follows. First, we consider the error incurred purely byquantization, i.e., rounding an original feature in the range of

to . We assume that the originalfeature distributed (approximately) uniformly over this range,leading to a mean-squared distortion of

(8)

This is the case when the LUT entry corresponding to the quan-tized version of the original feature equals to the bit to be em-bedded. We then consider the case thatdoes not map to thedesired bit value by LUT. In this situation, we have to shift thewatermarked feature to or in order to embed

the desired bit. For a half interval of anoriginal feature, maps to the desired bit by LUT andis output as watermarked feature with probability of

. On the other hand, with probability of, maps to the same value as does, and

that value does not equal to the desired bit. According to the runconstraint, must be mapped to the desired bit value andshould be output as the watermarked feature. By symmetry, theother half interval of an original featurecan be analyzed in the same way. The mean squared distortionwhen does not match to the desired bit value is thus

(9)

The probability terms andcan be computed from the Markovian model pre-

sented in Section III. If the Markov chain is initialized with thestationary probability (or equivalently,the initial status of the LUT generation is set to this probability),we have

(10)

Therefore

(11)


Fig. 2. Illustration of reduced detection errors of LUT embedding as themaximum allowable runr increases.

Since with probability of 1/2 the table lookup value ofmatches the desired bit, the overall MSE of the embedding is

(12)

We can see that using the quantization step size, LUT em-bedding with maximum run of 2 introduces MSE distortion of

, which is larger than the MSE distortion of by theodd-even embedding (or equivalently, LUT embedding with run1). However, with larger run in LUT, stronger noise dragging awatermarked feature out of the enforced interval does not neces-sarily lead to errors in detection. An example is shown in Fig. 2.When noise drags a watermarked featureaway to ,the extracted bit will have different value from the embeddedbit in the case of odd-even embedding (run 1). Such a detectionerror may not happen when the allowable run of LUT increasessince with some probability and are now mappedto the same bit value, as shown in Fig. 2. The probability of de-tection error can therefore be reduced. Next, we present analyticand experimental results on this issue.

B. Probability of Detection Error Under Additive WhiteGaussian Noise

To quantify the robustness in terms of the probability of de-tection error, we assume that the watermarked feature is atand that the additive noise follows i.i.d. Gaussian distribution

with zero mean and variance . The probability ofnoise pushing a feature to other intervals that are far away from

is small due to the fast decay of the tails of Gaussian distri-bution, so the probability of detection error can be approximatedby considering only the nearby intervals around. When noisedrags the watermarked feature away fromto , we will en-counter detection error only when .For LUT embedding with a maximum allowable run of 2, thereare three cases for the LUT entries of , , and :

• ;• ;•

Applying the Markovian property of LUT to computing the jointprobability

where , we find the probability of the first case as

(13)

(14)

Note that (14) is based on the stationary probability of theMarkov chain, which is valid either when the Markov chain isinitialized with the stationary probability, or whenapproachesinfinity. Similarly, we obtain the probability of the other twocases as

(15)

(16)

Thus, the probability of detection error under Gaussian noisecan be approximated by

(17)

(18)

where the Q-function is the tail probability of a Gaussianrandom variable . Defining the watermark-to-noise ratio(WNR) as the ratio of MSE distortion introduced by wa-termark embedding to that by additional noise, we have

for the LUT embedding with maximum allowable runaccording to (12). The probability of detection error of

(18) in terms of WNR becomes

(19)

This analytic approximation of the probability of detection errorvs. WNR is compared with the simulation result for maximumallowable run . We can see from Fig. 3 that the analyticapproximation and simulation conform very well.

In contrast, for LUT with a maximum run of 1 (or equiva-lently, the odd-even embedding), detection error occurs as soonas the noise is strong enough to drag the watermarked featureto the quantization intervals next to the interval. The proba-bility of detection errors for this embedding is

(20)

(21)

where the WNR .


Fig. 3. Analytic and simulation result of detection error probability underwhite Gaussian noise for LUT embedding with maximum allowable LUT runof 2.

Fig. 4. Detection error probability under white Gaussian noise for LUTembedding with different maximum allowable LUT runs.

Using a total of 500 000 simulation points at each WNRranging from 6 dB to 10 dB, we compare the probabilityof detection error versus WNR for maximum allowable run

of 1, 2, 3, and infinity, respectively. As can be seen fromFig. 4, of a maximum run of 2 (solid line) is significantlysmaller than a run of 1 (dot line) for up to 4-dB advantage atlow and medium WNR, and is slightly higher at high WNR.In addition, the further increase of LUT’s run (dotted-dashedline and dashed line) gives only a small amount of reductionof at low WNR and much larger at medium and highWNR. This indicates that LUT embedding with maximumallowable run of 2 can potentially provide higher robustness, aswell as higher security than the commonly used quantizationembedding with equivalent run 1. In the next section, weexplore techniques that further improve the robustness andcapacity of LUT embedding.

V. DISTORTION-COMPENSATEDLUT EMBEDDING

Motivated by Costa’s information theoretical result [11], dis-tortion compensation has been proposed and incorporated intoquantization-based embedding [10], [12]–[14], where the LUTenforced feature is combined linearly with the original featurevalue to form a watermarked feature. Using an optimal scalingfactor that is a function of WNR, distortion compensated versionof odd-even embedding provides higher capacity than withoutcompensation [10]. The basic idea behind such improvementis to render more separation between the watermarked featurevalues while keeping the mean square distortion introduced bythe embedding process unchanged. In this section, we proposeto apply distortion compensation to LUT embedding and studythe impact of distortion compensation on the reliability of LUTembedding.

A. Analysis of Probability of Detection Error

Let be the original unmarked feature, the output fromLUT embedding alone (with maximum allowable LUT run), and be the finally watermarked feature after distortion

compensation. We use a quantization step size ofto producein the LUT embedding step, where is also used

as a weighting factor in distortion compensation

(22)

When equals 1, this is reduced to the LUT embedding withquantization step size and without distortion compensation.The overall mean squared distortion introduced by this distor-tion compensated embedding is

(23)

In other words, the mean squared distortion by embedding re-mains the same as in the noncompensated version that uses aquantization step size of.

One criterion for selecting of is to maximize the following“SNR”:

(24)

Here, the “signal” power in the numerator is the mean squareddistance between two neighboring, perfectly enforced featurevalues representing “1” and “0”, and the “noise” power in the de-nominator is the mean squared deviation away from a perfectlyenforced feature, where the deviation is introduced by both dis-tortion compensation and additional noise of variance. The

value that maximizes the above SNR can be found as

(25)

We can see that in terms of a function of WNR, this optimumcompensation factor is identical to the distortion compensationcase studied by Chen–Wornell [10] where the equivalent run is1. We also note that a watermarking system under study usuallytargets at optimizing the embedding capacity at a specific noise


level. This will give a specific targeted WNR, and lead to anoptimal corresponding to this noise level. When the targetednoise level changes, so does the corresponding optimal.

To analyze the probability of detection error, we focus on thescenario when is in the interval of forsome , and study three cases of , namely (1) ,(2) , and (3) , respectively.As analyzed in the previous section, the conditional probabilityof each of these three cases is 1/2, 1/3, and 1/6, respectively. Inthe first case of , the watermarked feature

where . Under white Gaussian noise, the conditional probability of error can be further

broken down into three substantial terms that reflect differentcombinations of the , , and entries in theLUT table. This analysis approach is similar to the one usedin Section IV-B. Thus, the conditional probability of error forthis case becomes

(26)

(27)

Similarly, the conditional probability of error for the other twocases are given as follows:

(28)

(29)

Fig. 5. Analytic and simulation result of detection error probability underwhite Gaussian noise for distortion compensated LUT embedding withmaximum allowable run of 2.

The result of can be obtainedby symmetry. Therefore, we arrive at the overall probability ofdetection error as

(30)

(31)

where , and is the WNR. Because ofthe fast decay of as increases, we can further approxi-mate into four terms

(32)

Fig. 5 plots the probability of error versus the WNR fordistortion compensated LUT embedding with maximum allow-able run of 2. Solid line represents the numerical evaluation of(31), cross marks are approximations of (32), and the dashedline comes from our simulation of a total of 500 000 data pointsat each WNR setting. We can see that the analytic approxima-tions of (31) and (32) agree very well with the simulation re-sults especially at high WNR, while there is a small gap betweenthem at lower WNR. Including more LUT entries aroundin


Fig. 6. BSC embedding capacity under different maximum allowable LUTruns and different compensation settings.

our analysis will improve the approximation accuracy and re-duce this gap at low WNR.

Next, we jointly evaluate the robustness and security of theproposed distortion compensated LUT embedding with max-imum allowable run of 2 and of other embedding settings.

B. Joint Evaluation of Robustness and Security

We quantify the robustness of different embedding settingsthrough their embedding capacities at a wide range of WNRs.For simplicity, the channel between embedding and detection ismodeled as a simple, binary symmetric channel (BSC) [18] withcross-over probability being the probability of error studiedabove. That is

(33)

We compare the BSC embedding capacity of five casesin Fig. 6, namely, the maximum allowable run of 2 with andwithout distortion compensation, constant run of 1 (traditionalodd-even embedding) with and without compensation, andmaximum allowable run of infinity (i.e., no run constraint)with compensation. From the cross-marked line to the dashedline, we see that when the maximum allowable run is 2, theembedding capacity increases significantly for up to 4-dBadvantage in WNR after applying distortion compensation. Wealso observe that when keeping all other conditions identicaland only varying the maximum allowable run of LUT, theincrease in allowable run gives higher embedding capacity inlow WNR when no compensation is used (the dotted line to thecross marked line), and a moderately smaller capacity whendistortion compensation is applied (the solid line to the dashline to the circle line). For example, at comparable capacity,distortion compensated LUT embedding with maximum runof 2 requires about 1 dB more in WNR than the compensatedcase with run of 1. The intuition behind is as follows: the runconstraint of 1 with distortion compensation, or equivalentlythe scalar Costa’s embedding [14], gives near-optimal embed-ding capacity supported by information theoretical study [10],

Fig. 7. Linear joint security and capacity measure of LUT embedding as afunction of weight! at a WNR of 0 dB.

which concerns maximizing the capacity under a specific WNRwithout other considerations such as the security inherent inthe embedding mechanism in Section III. On the other hand,the case of run constraints of 2 provides extra uncertainty inthe embedding. As an expense, the error rate at the same WNRlevel is slightly higher, or equivalently, the embedding capacityis lower than the run-1 case. This shows a tradeoff betweencapacity and security, but the above embedding capacitycomparison alone, however, concerns mainly the robustnessand does not include information about security.

To take into account both security and robustness issues, wedefine a joint measure as a function of the entropyrate of the embedding mapping and the embedding capacity

. One simple choice of is a linear combination of theentropy rate and the embedding capacity under BSC assumptionfor additive noise. That is

(34)

where is the entropy rate of LUT table given by (6),is the BSC embedding capacity given by (33), and isa weight factor to provide desirable emphasis to security androbustness issues. We plot this joint measure at 0 dB WNRfor maximum LUT run of 1 and 2, respectively, with differentweight and different compensation settings. We can see fromFig. 7 that distortion compensated embedding with run con-straint of 2 (cross-marked line) gives the highestover a widerange of weight values. It holds until the weightgoing below0.15 or security is not much concerned, where the joint measurefor the traditional odd-even embedding with distortion compen-sation (dash line) becomes higher. The figure suggests that aslong as some level of security is desired, by slightly increasingthe allowable LUT run from 1 to 2 and by applying distortioncompensation, we can provide joint improvement of securityand robustness to quantization-based embedding.

C. Discussions

Variations of Distortion Compensation:We explore a fewvariations of distortion compensation and compare their perfor-


Fig. 8. Illustration of different distortion-compensation strategies.

Fig. 9. Comparison of probability of error of three compensation techniquesfor LUT embedding with maximum allowable run of 2.

mance with the linear compensation in (22). We shall focus onthe case of maximum allowable run of 2. As illustrated in Fig. 8,to embed a bit , the linear compensation technique interpo-lates between the enforced point (highlighted by a hexag-onal icon) and the original feature point (five-star icon). Toprevent the compensation step from introducing large deviationfrom the enforced point when , we propose twoalternatives to . One is a boundary point (diamond icon),and the other is a mirroring point (triangle icon).

Shown in Fig. 9 are the performances of boundary-point-based compensation (cross marks), mirroring-based compensa-tion (dot line), and the optimal linear compensation (solid line).The probabilities of detection error are comparable for thesethree compensation cases. The underlying reason is becausethe larger distortion introduced by embedding, such as in theoptimal linear compensation can also bring larger guard zonehence resist stronger distortion. This leads to nearly identicalrobustness of the above three compensation approaches whennormalized in terms of WNR.

Robustness Against Uniformly Distributed Noise:Primarilyintroduced by quantizing the watermarked signals, uniformlydistributed noise is common in data-hiding applications. Due tothe bounded nature of uniform noise, detection is error free untilthe range of noise exceeds half of the quantization step size.The probability of detection error under uniform noise for theodd-even embedding was analyzed in our previous work [19].For embedding with larger LUT runs and distortion compensa-tion, the robustness analysis against uniformly distributed addi-tive noise is similar to that for Gaussian noise presented earlierin this paper and will not be elaborated here. We present the

Fig. 10. Comparison of the probability of detection error under uniform versuswhite Gaussian noise for LUT embedding with maximum allowable run of 2 andlinear distortion compensation.

robustness comparison of LUT embedding against uniformnoise versus white Gaussian noise in Fig. 10, where the LUTembedding uses maximum allowable run of 2 and lineardistortion compensation. We see that the LUT embedding hassimilar robustness against uniform and Gaussian noise. Thequantization nature of LUT embedding, along with the boundedproperty of uniform noise, gives a zero-error region at veryhigh WNR; and the slightly higher error rate in medium WNRunder uniform noise can be reduced by soft detection [19].

VI. EXPERIMENTAL RESULTSWITH IMAGES

As a proof-of-concept, we apply our proposed distortion com-pensated LUT embedding with run constraint of 2 to the 512

512 Lenna image. One bit is embedded in each pixel, andthe embedded raw data forms a 512512 pattern shown inFig. 11(c). For comparison, we have also implemented a embed-ding scheme using the same LUT but without compensation,2

as well as the popular odd-even embedding with and withoutcompensation. The base quantization stepis 3 and the PSNRsof watermarked images are about 42 dB. Fig. 11(b) shows azoomed-in version of watermarked Lenna by the proposed em-bedding with LUT run constraint of 2 and linear distortion com-pensation.

Next, we add white Gaussian noise to watermarked imagesand tailor its strength to give a WNR of 0 dB in all tests. Thedetection errors on 512 512-bit raw data are visualized inFig. 12, from which we can see an improvement by distortioncompensation [Fig. 12(c) and (d)] on reducing the raw bit errorrate by 10%. We also note that when distortion compensationis applied, the error rate for run constraint of 1 [Fig. 12(c)] isslightly lower than that for run constraint of 2 [Fig. 12(d)]. Theseall confirm our analysis presented in Fig. 6 of Section V.

To overcome the bit errors in data extraction, channel codingcan be applied to provide reliable communication at targetedWNRs. Here, we visualize the effect of simple repetition coding

2This noncompensated scheme is similar to [2] but applied in quantizedpixels. For simplicity, we omit an error diffusion step that can further improvethe perceptual quality of watermarked images.


Fig. 11. A zoomed-in view of the (a) original Lenna image and (b) the watermarked version using distortion-compensated LUT embedding with run constraintof 2, along with (c) a 512� 512-bit pattern embedded in the Lenna image. The base quantization step is 3 and the PSNRs of the watermarked images are 42 dB.

(a) (b)

(c) (d)

Fig. 12. Visualization of raw error pattern by LUT embedding with different settings underWNR = 0dB. (a) Run= 1, no compensation, error 38.8%. (b) Run� 2, no compensation, error 35.1%. (c) Run= 1, with compensation, error 23.6%. (b) Run� 2, with compensation, error 26.0%.

followed by majority voting in decoding. As can be seen fromFig. 13, the 16-time repetition coding of a 128128-bit patterncan allow most bits extracted correctly, and the 64-time repeti-tion will deliver a 64 64-bit pattern free of error. The resultunder uniform noise at WNR 0 dB, shown in Fig. 13(c), is sim-ilar to that under white Gaussian noise. This is expected basedon our study in Section V-C.

Furthermore, we examine the effects of attacks other than ad-ditive white noise. In particular, we are interested in the perfor-mance under the popular JPEG compression. We apply JPEGcompression with quality factors 95% and 75%, respectively,to the watermarked image of Fig. 11. As shown in Fig. 14(a),the equivalent WNR of JPEG 95% quality is 0.5 dB and the rawerror rate before error correction coding is 24.5%, both of which


(a) (b) (c)

Fig. 13. Visualization of extracted data after applying repetition coding and majority voting underWNR = 0dB. The effective payloads are: (a) 64� 64 bitsand (b) and (c) 128� 128 bits. (a) 64 repetitions, Gaussian noise. (b) 16 repetitions, Gaussian noise. (c) 16 repetitions, uniform noise. The noise distribution is (a)and (b) white Gaussian and (c) white uniform.

(a)

(b)

Fig. 14. Visualization of extracted data from the watermarked image of Fig. 11after JPEG compression with two different quality factors: (a) JPEG 95% qualitywith equivalent WNR=0.5 dB and error rate before coding 24.5%. (b) JPEG75% quality with equivalent WNR= �6.25 dB and error rate before coding37.8%. 16-time repetition coding and majority voting is used, with an effectivepayload of 128� 128 bits.

are comparable to the additive noise case shown in Fig. 12 andFig. 13. When compression becomes stronger with respect tothe watermark, as in Fig. 14(b), the error rate before coding ishigher and requires more powerful coding to accurately extractthe effective payload. For the same level of compression, onecan increase the quantization step size and thus make the wa-termark stronger to reduce the raw error rate. This is a tradeoffbetween robustness, imperceptibility, and payload.

As a final note, the proposed LUT embedding with distortioncompensation can be combined with advanced coding such asthose in [13], [14] to improve the coding efficiency. It can also beapplied in transform domains such as the DCT and the Waveletdomain for improved tradeoff between imperceptibility, pay-load, and robustness against common processing.

VII. CONCLUSIONS

In summary, this paper studies the joint enhancement of se-curity and robustness for quantization-based data embedding.We start with a general embedding approach that employs aLUT mapping quantized multimedia features to binary data. Wequantify the security strength of LUT embedding in terms ofentropy rate and have shown that the security is improved sig-nificantly with a slight increase of the allowable LUT run from1 to 2. We present analysis showing that LUT embedding withlarger run constraints can have smaller probability of detectionerror for up to 4-dB advantage in WNR. We then explore dis-tortion compensation on LUT embedding to further enhance itsrobustness and provide an additional advantage of up to 4 dB inWNR. Through a joint security and capacity measure, we haveshown that our proposed distortion compensated LUT embed-ding with maximum allowable run of 2 offers joint enhancementof security and robustness over the traditional quantization em-bedding that has an equivalent run of 1. This joint enhancementmakes the proposed embedding scheme an attractive buildingblock for multimedia authentication applications.

APPENDIX

Proof of Theorem 1:The generation process of LUT tablecan be represented using an-ary tree, and equals tothe number of nodes in the level of this tree. Proving(3) is thus equivalent to count the nodes in Level- .First, we mark all the nodes that have different values fromtheir parent nodes. The number of nodes marked in this step is

. Next, for , among the unmarked nodes ofLevel- that have the same value as their parent nodes,

of them have a grandparent node and a parentnode that carry different values. Because the nodes’ valuechanges from grandparent level to parent level, the run is reset


there so that the run from parent to the current level does notexceed the constraint. We therefore mark these nodes, givinga total of marked nodes. We continuethis marking process for nodes that have continuous run of 3,

to mark all the nodes in Level- , giving a totalnumber of .

ACKNOWLEDGMENT

The author thanks Prof. B. Liu of Princeton University forinsightful discussions during the early exploration of lookuptable embedding, and anonymous reviewers for their construc-tive comments.

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[3] M. Holliman and N. Memon, “Counterfeiting attacks on obliviousblockwise independent invisible watermarking schemes,”IEEE Trans.Image Processing, vol. 9, pp. 432–441, Mar. 2000.

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[5] D. Kundur and D. Hatzinakos, “Digital watermarking for telltale tamper-proofing and authentication,”Proc. IEEE, vol. 87, pp. 1167–1180, July1999.

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[7] P. Yin and H. Yu, “Semi-fragile watermarking system for MPEG videoauthentication,” inProc. Int. Conf. Acoustics, Speech and Signal Pro-cessing (ICASSP), Orlando, FL, May 2002, pp. 3461–3464.

[8] I. Cox, J. Kilian, T. Leighton, and T. Shamoon, “Secure spread spectrumwatermarking for multimedia,”IEEE Trans. Image Processing, vol. 6,pp. 1673–1687, Dec. 1997.

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Min Wu (S’95–M’01) received the B.E. degreein electrical engineering and the B.A. degree ineconomics from Tsinghua University, Beijing,China, in 1996 (both with the highest honors), andthe M.A. and Ph.D. degrees in electrical engineeringfrom Princeton University, Princeton, NJ, in 1998and 2001, respectively.

She was with NEC Research Institute and Signafy,Inc. in 1998, and with Panasonic Information andNetworking Laboratories in 1999. Since 2001, shehas been an Assistant Professor of the Department of

Electrical and Computer Engineering, Institute of Advanced Computer Studies,and the Institute of Systems Research, both at the University of Maryland,College Park. Her research interests include information security, multimediasignal processing, and multimedia communications. She is co-author of thebook Multimedia Data Hiding(New York: Springer-Verlag, 2002) and holdsthree U.S. patents on multimedia data hiding.

Dr. Wu is a member of the IEEE Technical Committee on Multimedia SignalProcessing, Publicity Chair of the 2003 IEEE International Conference on Mul-timedia and Expo (ICME’03, Baltimore), and a Guest Editor of a Special Issueon Multimedia Security and Rights Management of theEURASIP Journal onApplied Signal Processing. She received a CAREER award from the U.S. Na-tional Science Foundation in 2002.

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